Slope of Parallel and Perpendicular Lines Notes and Worksheets ... - Free Printable

Let's go through each section of the "Finding Slope Notes" worksheet and fill in the blanks with correct explanations and solutions.

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1. When You Have a Graph

Example: A line is drawn on a coordinate grid, going from top-left to bottom-right (downward slope).

What to Do:
> Count rise over run on the graph.

- Explanation:
To find the slope from a graph, you use the rise over run method:
- Rise = change in y (vertical movement)
- Run = change in x (horizontal movement)

For this example, pick two points on the line. Let’s assume the line passes through (1, 4) and (3, 0) — based on the graph.
- Rise = 0 – 4 = –4
- Run = 3 – 1 = 2
- Slope = rise/run = –4/2 = –2

So, the slope is –2, which is negative (matches the downward trend).

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2. When You Have Two Points

Given Points: (2, 4) and (0, –7)

Use the slope formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Let’s assign:
- $ (x_1, y_1) = (2, 4) $
- $ (x_2, y_2) = (0, -7) $

Now plug into the formula:
$$
m = \frac{-7 - 4}{0 - 2} = \frac{-11}{-2} = \frac{11}{2}
$$

✔ Slope = $ \frac{11}{2} $ or 5.5

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3. When You Have the Equation in Standard Form: $ 2x + 3y = 10 $

What to Do:
> Change equation to slope-intercept form.

- Slope-intercept form: $ y = mx + b $

Let’s solve for $ y $:

$$
2x + 3y = 10
$$
Subtract $ 2x $ from both sides:
$$
3y = -2x + 10
$$
Divide by 3:
$$
y = -\frac{2}{3}x + \frac{10}{3}
$$

✔ So, the slope $ m = -\frac{2}{3} $

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4. When You Have the Equation in Slope-Intercept Form: $ y = 3x + 7 $

What to Do:
> Just find “m”!

- In $ y = mx + b $, m is the coefficient of x.

So, here:
$$
m = 3
$$

✔ Slope = 3

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✔ Final Summary of Answers:

| Scenario | What to Do | Answer |
|--------|------------|--------|
| Graph | Count rise over run | Slope = –2 (example) |
| Two Points (2,4), (0,-7) | Use slope formula | $ m = \frac{11}{2} $ |
| Standard form: $ 2x + 3y = 10 $ | Change to slope-intercept form | $ m = -\frac{2}{3} $ |
| Slope-intercept: $ y = 3x + 7 $ | Just find “m” | $ m = 3 $ |

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🔍 Additional Notes:

- Positive slope: Line goes up from left to right.
- Negative slope: Line goes down from left to right.
- Zero slope: Horizontal line (no rise).
- Undefined slope: Vertical line (no run).

This worksheet helps students recognize how to find slope in different situations — from graphs, points, equations, etc. The key idea is that slope = rate of change = rise/run.

Let me know if you'd like this turned into a printable answer key!